MinT - Best Known (167−105, 167, s)-Nets in Base 8

Best Known (167−105, 167, s)-Nets in Base 8

(167−105, 167, 98)-Net over F₈ — Constructive and digital

Digital (62, 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]

(167−105, 167, 144)-Net over F₈ — Digital

Digital (62, 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]

(167−105, 167, 2173)-Net in Base 8 — Upper bound on s

There is no (62, 167, 2174)-net in base 8, because

1 times m-reduction [i] would yield (62, 166, 2174)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 820207 156021 995501 341216 933849 453290 606518 200603 573515 346900 067248 569719 527524 312664 909648 590021 012501 824195 356121 211720 298715 951053 903028 140679 223467 > 8¹⁶⁶ [i]