MinT - Best Known (131−84, 131, s)-Nets in Base 8

Best Known (131−84, 131, s)-Nets in Base 8

(131−84, 131, 98)-Net over F₈ — Constructive and digital

Digital (47, 131, 98)-net over F₈, using

t-expansion [i] based on digital (37, 131, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(131−84, 131, 144)-Net over F₈ — Digital

Digital (47, 131, 144)-net over F₈, using

t-expansion [i] based on digital (45, 131, 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]

(131−84, 131, 1520)-Net in Base 8 — Upper bound on s

There is no (47, 131, 1521)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20384 888285 207140 515996 048623 366754 702698 178368 010884 358505 949210 263918 476682 361684 745478 157819 451060 917074 432716 493352 > 8¹³¹ [i]