MinT - Best Known (257−117, 257, s)-Nets in Base 4

Best Known (257−117, 257, s)-Nets in Base 4

(257−117, 257, 130)-Net over F₄ — Constructive and digital

Digital (140, 257, 130)-net over F₄, using

t-expansion [i] based on digital (105, 257, 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]

(257−117, 257, 241)-Net over F₄ — Digital

Digital (140, 257, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−117, 257, 3352)-Net in Base 4 — Upper bound on s

There is no (140, 257, 3353)-net in base 4, because

1 times m-reduction [i] would yield (140, 256, 3353)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13549 411019 696508 341736 222445 739667 963651 439911 417434 768218 897994 197574 259048 165217 342135 012467 640052 054440 575933 695869 974113 047600 176434 677935 101664 098560 > 4²⁵⁶ [i]