MinT - Best Known (236−128, 236, s)-Nets in Base 4

Best Known (236−128, 236, s)-Nets in Base 4

(236−128, 236, 130)-Net over F₄ — Constructive and digital

Digital (108, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(236−128, 236, 144)-Net over F₄ — Digital

Digital (108, 236, 144)-net over F₄, using

t-expansion [i] based on digital (91, 236, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(236−128, 236, 1313)-Net in Base 4 — Upper bound on s

There is no (108, 236, 1314)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12664 309406 314349 306441 286858 211976 577749 919016 521764 362077 556972 693302 915206 248139 001833 939920 018383 698935 272033 824301 460685 295573 716458 802116 > 4²³⁶ [i]