MinT - Best Known (203−87, 203, s)-Nets in Base 4

Best Known (203−87, 203, s)-Nets in Base 4

(203−87, 203, 130)-Net over F₄ — Constructive and digital

Digital (116, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(203−87, 203, 237)-Net over F₄ — Digital

Digital (116, 203, 237)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−87, 203, 3754)-Net in Base 4 — Upper bound on s

There is no (116, 203, 3755)-net in base 4, because

1 times m-reduction [i] would yield (116, 202, 3755)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 455007 437422 071763 458916 645766 203916 486921 019756 306873 520049 783889 544227 916378 911355 889608 309836 493524 174385 028194 487036 > 4²⁰² [i]