MinT - Best Known (230−101, 230, s)-Nets in Base 4

Best Known (230−101, 230, s)-Nets in Base 4

(230−101, 230, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(230−101, 230, 245)-Net over F₄ — Digital

Digital (129, 230, 245)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−101, 230, 3674)-Net in Base 4 — Upper bound on s

There is no (129, 230, 3675)-net in base 4, because

1 times m-reduction [i] would yield (129, 229, 3675)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 752892 952535 223487 762499 665035 038677 940123 482587 736207 010113 773536 312011 961785 625231 219728 277048 445762 521345 896015 099514 331071 866433 488990 > 4²²⁹ [i]