MinT - Best Known (124−77, 124, s)-Nets in Base 8

Best Known (124−77, 124, s)-Nets in Base 8

(124−77, 124, 98)-Net over F₈ — Constructive and digital

Digital (47, 124, 98)-net over F₈, using

t-expansion [i] based on digital (37, 124, 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]

(124−77, 124, 144)-Net over F₈ — Digital

Digital (47, 124, 144)-net over F₈, using

t-expansion [i] based on digital (45, 124, 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]

(124−77, 124, 1774)-Net in Base 8 — Upper bound on s

There is no (47, 124, 1775)-net in base 8, because

1 times m-reduction [i] would yield (47, 123, 1775)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1215 757483 855947 382590 499088 863993 431592 211383 634811 819077 253369 752554 643424 730029 552883 620163 202796 700508 875013 > 8¹²³ [i]