MinT - Best Known (236−127, 236, s)-Nets in Base 4

Best Known (236−127, 236, s)-Nets in Base 4

(236−127, 236, 130)-Net over F₄ — Constructive and digital

Digital (109, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(236−127, 236, 165)-Net over F₄ — Digital

Digital (109, 236, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(236−127, 236, 1375)-Net in Base 4 — Upper bound on s

There is no (109, 236, 1376)-net in base 4, because

1 times m-reduction [i] would yield (109, 235, 1376)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3130 917013 078921 558560 235561 139295 024881 489675 305034 872996 380031 230315 055424 933722 351333 106410 253972 369995 001802 024149 648613 146277 639011 107054 > 4²³⁵ [i]