MinT - Best Known (236−129, 236, s)-Nets in Base 4

Best Known (236−129, 236, s)-Nets in Base 4

(236−129, 236, 130)-Net over F₄ — Constructive and digital

Digital (107, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(236−129, 236, 144)-Net over F₄ — Digital

Digital (107, 236, 144)-net over F₄, using

t-expansion [i] based on digital (91, 236, 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]

(236−129, 236, 1283)-Net in Base 4 — Upper bound on s

There is no (107, 236, 1284)-net in base 4, because

1 times m-reduction [i] would yield (107, 235, 1284)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3055 140724 094603 442669 436905 716787 565669 647952 456909 239154 839132 831242 573386 570368 305912 268293 076711 716270 486873 912790 934042 371829 378084 187020 > 4²³⁵ [i]