MinT - Best Known (123, 123+113, s)-Nets in Base 4

Best Known (123, 123+113, s)-Nets in Base 4

(123, 123+113, 130)-Net over F₄ — Constructive and digital

Digital (123, 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]

(123, 123+113, 191)-Net over F₄ — Digital

Digital (123, 236, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+113, 2386)-Net in Base 4 — Upper bound on s

There is no (123, 236, 2387)-net in base 4, because

1 times m-reduction [i] would yield (123, 235, 2387)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3084 825950 223312 562580 378696 563352 729864 640951 208875 736280 017629 257478 052120 975085 188934 302155 203480 927263 412746 972175 457843 715253 344301 017960 > 4²³⁵ [i]