MinT - Best Known (113−62, 113, s)-Nets in Base 4

Best Known (113−62, 113, s)-Nets in Base 4

(113−62, 113, 66)-Net over F₄ — Constructive and digital

Digital (51, 113, 66)-net over F₄, using

t-expansion [i] based on digital (49, 113, 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]

(113−62, 113, 91)-Net over F₄ — Digital

Digital (51, 113, 91)-net over F₄, using

t-expansion [i] based on digital (50, 113, 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]

(113−62, 113, 622)-Net in Base 4 — Upper bound on s

There is no (51, 113, 623)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 108 078052 756160 095898 779966 955996 440234 137465 332234 499126 113427 409000 > 4¹¹³ [i]