MinT - Best Known (234−114, 234, s)-Nets in Base 4

Best Known (234−114, 234, s)-Nets in Base 4

(234−114, 234, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(234−114, 234, 179)-Net over F₄ — Digital

Digital (120, 234, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−114, 234, 2133)-Net in Base 4 — Upper bound on s

There is no (120, 234, 2134)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 771 249049 549320 125723 879505 537563 556322 122528 441237 478092 035904 380328 094833 940836 633418 774485 915071 285438 288236 105748 979177 455922 153970 223560 > 4²³⁴ [i]