MinT - Best Known (166−100, 166, s)-Nets in Base 8

Best Known (166−100, 166, s)-Nets in Base 8

(166−100, 166, 98)-Net over F₈ — Constructive and digital

Digital (66, 166, 98)-net over F₈, using

t-expansion [i] based on digital (37, 166, 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]

(166−100, 166, 144)-Net over F₈ — Digital

Digital (66, 166, 144)-net over F₈, using

t-expansion [i] based on digital (45, 166, 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]

(166−100, 166, 2740)-Net in Base 8 — Upper bound on s

There is no (66, 166, 2741)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 823509 800505 708618 113127 364189 217860 314610 348543 221726 054521 049434 872501 187081 065507 869089 440732 551819 651820 793998 913527 554497 635723 514850 401578 484166 > 8¹⁶⁶ [i]