MinT - Best Known (114−63, 114, s)-Nets in Base 8

Best Known (114−63, 114, s)-Nets in Base 8

(114−63, 114, 98)-Net over F₈ — Constructive and digital

Digital (51, 114, 98)-net over F₈, using

t-expansion [i] based on digital (37, 114, 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]

(114−63, 114, 144)-Net over F₈ — Digital

Digital (51, 114, 144)-net over F₈, using

t-expansion [i] based on digital (45, 114, 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]

(114−63, 114, 3454)-Net in Base 8 — Upper bound on s

There is no (51, 114, 3455)-net in base 8, because

1 times m-reduction [i] would yield (51, 113, 3455)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 122725 303198 546731 648449 565358 788394 026815 130258 564254 056631 720481 421773 802258 693087 253286 873741 441512 > 8¹¹³ [i]