MinT - Best Known (130, 130+109, s)-Nets in Base 4

Best Known (130, 130+109, s)-Nets in Base 4

(130, 130+109, 130)-Net over F₄ — Constructive and digital

Digital (130, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(130, 130+109, 225)-Net over F₄ — Digital

Digital (130, 239, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+109, 3103)-Net in Base 4 — Upper bound on s

There is no (130, 239, 3104)-net in base 4, because

1 times m-reduction [i] would yield (130, 238, 3104)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 198175 909599 898308 658437 446161 831073 717996 470615 884326 663736 597882 910485 877938 082480 482973 644497 991857 038836 624538 805587 427190 631026 776525 297824 > 4²³⁸ [i]