MinT - Best Known (230−99, 230, s)-Nets in Base 4

Best Known (230−99, 230, s)-Nets in Base 4

(230−99, 230, 130)-Net over F₄ — Constructive and digital

Digital (131, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−99, 230, 261)-Net over F₄ — Digital

Digital (131, 230, 261)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−99, 230, 4108)-Net in Base 4 — Upper bound on s

There is no (131, 230, 4109)-net in base 4, because

1 times m-reduction [i] would yield (131, 229, 4109)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 749909 569722 808270 635416 838333 641913 072069 819185 436812 846108 787204 456931 639367 221196 838048 210922 487544 979548 074330 958210 767320 036695 648256 > 4²²⁹ [i]