MinT - Best Known (142−99, 142, s)-Nets in Base 8

Best Known (142−99, 142, s)-Nets in Base 8

(142−99, 142, 98)-Net over F₈ — Constructive and digital

Digital (43, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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]

(142−99, 142, 129)-Net over F₈ — Digital

Digital (43, 142, 129)-net over F₈, using

t-expansion [i] based on digital (38, 142, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(142−99, 142, 1052)-Net in Base 8 — Upper bound on s

There is no (43, 142, 1053)-net in base 8, because

1 times m-reduction [i] would yield (43, 141, 1053)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 722352 118962 106560 192487 914600 660906 515441 341604 179304 674549 929366 233263 607565 596197 925707 428263 449454 532803 106878 834050 595968 > 8¹⁴¹ [i]