MinT - Best Known (59, 59+141, s)-Nets in Base 4

Best Known (59, 59+141, s)-Nets in Base 4

(59, 59+141, 66)-Net over F₄ — Constructive and digital

Digital (59, 200, 66)-net over F₄, using

t-expansion [i] based on digital (49, 200, 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]

(59, 59+141, 91)-Net over F₄ — Digital

Digital (59, 200, 91)-net over F₄, using

t-expansion [i] based on digital (50, 200, 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]

(59, 59+141, 406)-Net in Base 4 — Upper bound on s

There is no (59, 200, 407)-net in base 4, because

1 times m-reduction [i] would yield (59, 199, 407)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 725713 693035 929161 081851 034545 832943 961631 902381 315931 585833 575233 586119 349799 154184 568628 925992 213858 600789 435445 042770 > 4¹⁹⁹ [i]