MinT - Best Known (65, 157, s)-Nets in Base 8

Best Known (65, 157, s)-Nets in Base 8

(65, 157, 98)-Net over F₈ — Constructive and digital

Digital (65, 157, 98)-net over F₈, using

t-expansion [i] based on digital (37, 157, 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]

(65, 157, 144)-Net over F₈ — Digital

Digital (65, 157, 144)-net over F₈, using

t-expansion [i] based on digital (45, 157, 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]

(65, 157, 3078)-Net in Base 8 — Upper bound on s

There is no (65, 157, 3079)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6137 565123 864794 075582 594548 081574 014782 479164 325867 233879 705181 012736 345178 147480 080284 590602 736639 469802 739543 258536 191952 392242 202463 404416 > 8¹⁵⁷ [i]