MinT - Best Known (77−46, 77, s)-Nets in Base 81

Best Known (77−46, 77, s)-Nets in Base 81

(77−46, 77, 370)-Net over F₈₁ — Constructive and digital

Digital (31, 77, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 77, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(77−46, 77, 551)-Net over F₈₁ — Digital

Digital (31, 77, 551)-net over F₈₁, using

t-expansion [i] based on digital (30, 77, 551)-net over F₈₁, using
- net from sequence [i] based on digital (30, 550)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 30 and N(F) ≥ 551, using
    - a curve from the manYPoints database [i]

(77−46, 77, 288818)-Net in Base 81 — Upper bound on s

There is no (31, 77, 288819)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 898 169116 534221 891105 343374 009984 971466 662274 040988 940469 841978 261243 132650 749124 040899 830713 849218 526069 363402 895713 470937 532351 539582 290229 154961 > 81⁷⁷ [i]