MinT - Best Known (148−85, 148, s)-Nets in Base 8

Best Known (148−85, 148, s)-Nets in Base 8

(148−85, 148, 99)-Net over F₈ — Constructive and digital

Digital (63, 148, 99)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 49, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (14, 99, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(148−85, 148, 144)-Net over F₈ — Digital

Digital (63, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(148−85, 148, 150)-Net in Base 8

(63, 148, 150)-net in base 8, using

base change [i] based on digital (26, 111, 150)-net over F₁₆, using
- net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
    - a curve from the manYPoints database [i]

(148−85, 148, 3389)-Net in Base 8 — Upper bound on s

There is no (63, 148, 3390)-net in base 8, because

1 times m-reduction [i] would yield (63, 147, 3390)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 708551 754156 906658 421883 022094 192803 613843 402202 567455 624211 560479 551814 330730 326239 560197 928288 442391 684228 380530 853281 224361 538598 > 8¹⁴⁷ [i]