MinT - Best Known (167−104, 167, s)-Nets in Base 8

Best Known (167−104, 167, s)-Nets in Base 8

(167−104, 167, 98)-Net over F₈ — Constructive and digital

Digital (63, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(167−104, 167, 144)-Net over F₈ — Digital

Digital (63, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(167−104, 167, 2263)-Net in Base 8 — Upper bound on s

There is no (63, 167, 2264)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 557205 619407 092456 408630 179017 948331 869148 105574 099491 810531 396655 213266 928393 836688 728056 569851 908462 135404 367488 261721 857595 668288 566442 872852 766658 > 8¹⁶⁷ [i]