MinT - Best Known (220−103, 220, s)-Nets in Base 4

Best Known (220−103, 220, s)-Nets in Base 4

(220−103, 220, 130)-Net over F₄ — Constructive and digital

Digital (117, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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]

(220−103, 220, 192)-Net over F₄ — Digital

Digital (117, 220, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−103, 220, 2505)-Net in Base 4 — Upper bound on s

There is no (117, 220, 2506)-net in base 4, because

1 times m-reduction [i] would yield (117, 219, 2506)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 718499 902808 801086 426534 638799 912168 962711 475977 868689 896736 237068 422283 911124 641980 602085 647944 655991 670413 461879 067918 230922 640624 > 4²¹⁹ [i]