MinT - Best Known (144−82, 144, s)-Nets in Base 8

Best Known (144−82, 144, s)-Nets in Base 8

(144−82, 144, 99)-Net over F₈ — Constructive and digital

Digital (62, 144, 99)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 48, 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, 96, 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]

(144−82, 144, 144)-Net over F₈ — Digital

Digital (62, 144, 144)-net over F₈, using

t-expansion [i] based on digital (45, 144, 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]

(144−82, 144, 150)-Net in Base 8

(62, 144, 150)-net in base 8, using

base change [i] based on digital (26, 108, 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]

(144−82, 144, 3399)-Net in Base 8 — Upper bound on s

There is no (62, 144, 3400)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11215 576194 289904 633629 546467 407992 795184 017952 051266 535185 692202 588465 911222 033131 955939 204460 771581 690298 763434 809897 967879 420888 > 8¹⁴⁴ [i]