MinT - Best Known (114−55, 114, s)-Nets in Base 4

Best Known (114−55, 114, s)-Nets in Base 4

(114−55, 114, 66)-Net over F₄ — Constructive and digital

Digital (59, 114, 66)-net over F₄, using

t-expansion [i] based on digital (49, 114, 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]

(114−55, 114, 100)-Net over F₄ — Digital

Digital (59, 114, 100)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−55, 114, 1183)-Net in Base 4 — Upper bound on s

There is no (59, 114, 1184)-net in base 4, because

1 times m-reduction [i] would yield (59, 113, 1184)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 109 693300 044965 441473 676591 937482 001598 171024 840447 665173 319328 339375 > 4¹¹³ [i]