MinT - Best Known (234−108, 234, s)-Nets in Base 4

Best Known (234−108, 234, s)-Nets in Base 4

(234−108, 234, 130)-Net over F₄ — Constructive and digital

Digital (126, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−108, 234, 213)-Net over F₄ — Digital

Digital (126, 234, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−108, 234, 2795)-Net in Base 4 — Upper bound on s

There is no (126, 234, 2796)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 720048 952311 304787 461454 249715 001151 614979 670131 877328 360908 964506 943541 654980 693324 623925 310952 505289 846666 964638 905174 283493 478237 344280 > 4²³⁴ [i]