MinT - Best Known (258−129, 258, s)-Nets in Base 4

Best Known (258−129, 258, s)-Nets in Base 4

(258−129, 258, 130)-Net over F₄ — Constructive and digital

Digital (129, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(258−129, 258, 180)-Net over F₄ — Digital

Digital (129, 258, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−129, 258, 2099)-Net in Base 4 — Upper bound on s

There is no (129, 258, 2100)-net in base 4, because

1 times m-reduction [i] would yield (129, 257, 2100)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54789 174324 855812 200766 083512 003900 061587 171910 294038 678300 134343 817340 941217 397129 875806 422353 534907 540908 210597 410679 406406 091944 324637 410141 912818 322720 > 4²⁵⁷ [i]