MinT - Best Known (163−104, 163, s)-Nets in Base 4

Best Known (163−104, 163, s)-Nets in Base 4

(163−104, 163, 66)-Net over F₄ — Constructive and digital

Digital (59, 163, 66)-net over F₄, using

t-expansion [i] based on digital (49, 163, 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]

(163−104, 163, 91)-Net over F₄ — Digital

Digital (59, 163, 91)-net over F₄, using

t-expansion [i] based on digital (50, 163, 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]

(163−104, 163, 478)-Net in Base 4 — Upper bound on s

There is no (59, 163, 479)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 144 313724 663995 581660 253385 895752 484880 640068 943079 687904 972357 544092 305023 435617 720001 735362 199290 > 4¹⁶³ [i]