MinT - Best Known (118−71, 118, s)-Nets in Base 8

Best Known (118−71, 118, s)-Nets in Base 8

(118−71, 118, 98)-Net over F₈ — Constructive and digital

Digital (47, 118, 98)-net over F₈, using

t-expansion [i] based on digital (37, 118, 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]

(118−71, 118, 144)-Net over F₈ — Digital

Digital (47, 118, 144)-net over F₈, using

t-expansion [i] based on digital (45, 118, 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]

(118−71, 118, 2053)-Net in Base 8 — Upper bound on s

There is no (47, 118, 2054)-net in base 8, because

1 times m-reduction [i] would yield (47, 117, 2054)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4641 258617 658770 326768 986996 847506 115382 355739 061960 354922 532865 599312 774730 963701 529228 113349 979437 755008 > 8¹¹⁷ [i]