MinT - Best Known (190−130, 190, s)-Nets in Base 4

Best Known (190−130, 190, s)-Nets in Base 4

(190−130, 190, 66)-Net over F₄ — Constructive and digital

Digital (60, 190, 66)-net over F₄, using

t-expansion [i] based on digital (49, 190, 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]

(190−130, 190, 91)-Net over F₄ — Digital

Digital (60, 190, 91)-net over F₄, using

t-expansion [i] based on digital (50, 190, 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]

(190−130, 190, 428)-Net in Base 4 — Upper bound on s

There is no (60, 190, 429)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 551573 677401 901680 974735 794192 161339 759656 429008 633105 478622 869288 646238 631952 099540 684121 504566 532270 485635 815472 > 4¹⁹⁰ [i]