MinT - Best Known (195−137, 195, s)-Nets in Base 4

Best Known (195−137, 195, s)-Nets in Base 4

(195−137, 195, 66)-Net over F₄ — Constructive and digital

Digital (58, 195, 66)-net over F₄, using

t-expansion [i] based on digital (49, 195, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(195−137, 195, 91)-Net over F₄ — Digital

Digital (58, 195, 91)-net over F₄, using

t-expansion [i] based on digital (50, 195, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(195−137, 195, 401)-Net in Base 4 — Upper bound on s

There is no (58, 195, 402)-net in base 4, because

1 times m-reduction [i] would yield (58, 194, 402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 689 932651 979590 680391 331709 341000 781763 769957 016462 644799 893704 173374 365470 079641 973830 689226 424053 615379 159878 468760 > 4¹⁹⁴ [i]