MinT - Best Known (49, 49+83, s)-Nets in Base 8

Best Known (49, 49+83, s)-Nets in Base 8

(49, 49+83, 98)-Net over F₈ — Constructive and digital

Digital (49, 132, 98)-net over F₈, using

t-expansion [i] based on digital (37, 132, 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]

(49, 49+83, 144)-Net over F₈ — Digital

Digital (49, 132, 144)-net over F₈, using

t-expansion [i] based on digital (45, 132, 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]

(49, 49+83, 1745)-Net in Base 8 — Upper bound on s

There is no (49, 132, 1746)-net in base 8, because

1 times m-reduction [i] would yield (49, 131, 1746)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20371 274510 640935 034212 004573 490586 694302 020138 783849 164699 725024 852081 725495 109033 884970 448615 948053 493854 447414 141028 > 8¹³¹ [i]