MinT - Best Known (138, 255, s)-Nets in Base 4

Best Known (138, 255, s)-Nets in Base 4

(138, 255, 130)-Net over F₄ — Constructive and digital

Digital (138, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(138, 255, 234)-Net over F₄ — Digital

Digital (138, 255, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 255, 3193)-Net in Base 4 — Upper bound on s

There is no (138, 255, 3194)-net in base 4, because

1 times m-reduction [i] would yield (138, 254, 3194)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 842 637021 741812 588351 537188 144947 637935 964539 515214 790681 437195 252411 252579 234814 832557 279772 308502 464317 066207 466486 489670 705973 445518 320440 193408 718328 > 4²⁵⁴ [i]