MinT - Best Known (244−119, 244, s)-Nets in Base 4

Best Known (244−119, 244, s)-Nets in Base 4

(244−119, 244, 130)-Net over F₄ — Constructive and digital

Digital (125, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−119, 244, 185)-Net over F₄ — Digital

Digital (125, 244, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−119, 244, 2247)-Net in Base 4 — Upper bound on s

There is no (125, 244, 2248)-net in base 4, because

1 times m-reduction [i] would yield (125, 243, 2248)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 203 498322 956786 843514 311889 052943 283892 611326 126828 109669 938034 852105 918362 435944 138105 610902 386420 496415 569666 993493 826238 570996 480495 635611 101816 > 4²⁴³ [i]