MinT - Best Known (148−83, 148, s)-Nets in Base 8

Best Known (148−83, 148, s)-Nets in Base 8

(148−83, 148, 111)-Net over F₈ — Constructive and digital

Digital (65, 148, 111)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (10, 51, 46)-net over F₈, using
  - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
2. digital (14, 97, 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]

(148−83, 148, 152)-Net over F₈ — Digital

Digital (65, 148, 152)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−83, 148, 156)-Net in Base 8

(65, 148, 156)-net in base 8, using

4 times m-reduction [i] based on (65, 152, 156)-net in base 8, using
- base change [i] based on digital (27, 114, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(148−83, 148, 3961)-Net in Base 8 — Upper bound on s

There is no (65, 148, 3962)-net in base 8, because

1 times m-reduction [i] would yield (65, 147, 3962)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 684422 372380 160324 050517 340467 083008 057422 925724 326521 296243 619288 549352 668800 605680 620802 658554 105469 022028 992126 058128 164513 210785 > 8¹⁴⁷ [i]