MinT - Best Known (126, 126+134, s)-Nets in Base 4

Best Known (126, 126+134, s)-Nets in Base 4

(126, 126+134, 130)-Net over F₄ — Constructive and digital

Digital (126, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(126, 126+134, 176)-Net over F₄ — Digital

Digital (126, 260, 176)-net over F₄, using

t-expansion [i] based on digital (125, 260, 176)-net over F₄, using
- net from sequence [i] based on digital (125, 175)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
    - Drinfeld modules of rank 1 [i]

(126, 126+134, 1809)-Net in Base 4 — Upper bound on s

There is no (126, 260, 1810)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 437365 099957 416695 838576 615188 196928 190739 618664 417463 550430 572680 991471 562989 401128 939586 829339 196910 256357 110859 455420 816579 909491 311018 083436 464119 797664 > 4²⁶⁰ [i]