MinT - Best Known (167−120, 167, s)-Nets in Base 8

Best Known (167−120, 167, s)-Nets in Base 8

(167−120, 167, 98)-Net over F₈ — Constructive and digital

Digital (47, 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]

(167−120, 167, 144)-Net over F₈ — Digital

Digital (47, 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]

(167−120, 167, 1043)-Net in Base 8 — Upper bound on s

There is no (47, 167, 1044)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 783171 418074 544310 337519 363068 346722 366211 116248 895698 096455 350783 892542 289330 173555 703040 935148 758323 536885 733298 687649 421073 522164 599190 020780 509952 > 8¹⁶⁷ [i]