MinT - Best Known (105, 105+129, s)-Nets in Base 4

Best Known (105, 105+129, s)-Nets in Base 4

(105, 105+129, 130)-Net over F₄ — Constructive and digital

Digital (105, 234, 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]

(105, 105+129, 144)-Net over F₄ — Digital

Digital (105, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(105, 105+129, 1227)-Net in Base 4 — Upper bound on s

There is no (105, 234, 1228)-net in base 4, because

1 times m-reduction [i] would yield (105, 233, 1228)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 196 868319 460579 593234 447282 976606 335863 065074 893334 472345 122486 117183 115972 979640 548379 449793 061869 654339 035982 122456 362622 832612 057050 658151 > 4²³³ [i]