MinT - Best Known (151−89, 151, s)-Nets in Base 8

Best Known (151−89, 151, s)-Nets in Base 8

(151−89, 151, 98)-Net over F₈ — Constructive and digital

Digital (62, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(151−89, 151, 144)-Net over F₈ — Digital

Digital (62, 151, 144)-net over F₈, using

t-expansion [i] based on digital (45, 151, 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]

(151−89, 151, 2927)-Net in Base 8 — Upper bound on s

There is no (62, 151, 2928)-net in base 8, because

1 times m-reduction [i] would yield (62, 150, 2928)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2943 146572 889060 377487 940171 318414 892720 507977 562026 088447 527778 146323 046311 411771 029687 423087 773739 984543 938705 446640 413384 288493 865881 > 8¹⁵⁰ [i]