MinT - Best Known (42, 42+73, s)-Nets in Base 8

Best Known (42, 42+73, s)-Nets in Base 8

(42, 42+73, 98)-Net over F₈ — Constructive and digital

Digital (42, 115, 98)-net over F₈, using

t-expansion [i] based on digital (37, 115, 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]

(42, 42+73, 129)-Net over F₈ — Digital

Digital (42, 115, 129)-net over F₈, using

t-expansion [i] based on digital (38, 115, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(42, 42+73, 1454)-Net in Base 8 — Upper bound on s

There is no (42, 115, 1455)-net in base 8, because

1 times m-reduction [i] would yield (42, 114, 1455)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9 044398 410240 496388 107680 283891 057082 968904 632374 640451 257170 440517 277334 940372 522624 411718 058583 824521 > 8¹¹⁴ [i]