MinT - Best Known (127, 127+93, s)-Nets in Base 4

Best Known (127, 127+93, s)-Nets in Base 4

(127, 127+93, 130)-Net over F₄ — Constructive and digital

Digital (127, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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]

(127, 127+93, 266)-Net over F₄ — Digital

Digital (127, 220, 266)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+93, 4372)-Net in Base 4 — Upper bound on s

There is no (127, 220, 4373)-net in base 4, because

1 times m-reduction [i] would yield (127, 219, 4373)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 715150 700562 572154 574461 805379 113429 643529 054101 281229 640644 130255 386461 399572 723206 367063 584024 581907 150505 334128 283924 947002 895040 > 4²¹⁹ [i]