MinT - Best Known (245−113, 245, s)-Nets in Base 4

Best Known (245−113, 245, s)-Nets in Base 4

(245−113, 245, 130)-Net over F₄ — Constructive and digital

Digital (132, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−113, 245, 222)-Net over F₄ — Digital

Digital (132, 245, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−113, 245, 2993)-Net in Base 4 — Upper bound on s

There is no (132, 245, 2994)-net in base 4, because

1 times m-reduction [i] would yield (132, 244, 2994)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 807 324333 379712 110096 921925 527278 538826 746670 986436 533229 896797 042936 073513 358809 311018 446204 089826 742505 063230 772985 579733 814994 517818 689177 696624 > 4²⁴⁴ [i]