MinT - Best Known (128, 128+105, s)-Nets in Base 4

Best Known (128, 128+105, s)-Nets in Base 4

(128, 128+105, 130)-Net over F₄ — Constructive and digital

Digital (128, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(128, 128+105, 228)-Net over F₄ — Digital

Digital (128, 233, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+105, 3229)-Net in Base 4 — Upper bound on s

There is no (128, 233, 3230)-net in base 4, because

1 times m-reduction [i] would yield (128, 232, 3230)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 668274 036918 459062 374195 482721 231577 168018 191532 358342 375212 436683 352330 807116 387246 724910 728929 575443 394990 384839 907043 935262 653249 340516 > 4²³² [i]