MinT - Best Known (208−103, 208, s)-Nets in Base 4

Best Known (208−103, 208, s)-Nets in Base 4

(208−103, 208, 130)-Net over F₄ — Constructive and digital

Digital (105, 208, 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]

(208−103, 208, 153)-Net over F₄ — Digital

Digital (105, 208, 153)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−103, 208, 1796)-Net in Base 4 — Upper bound on s

There is no (105, 208, 1797)-net in base 4, because

1 times m-reduction [i] would yield (105, 207, 1797)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42838 955466 342708 379620 293404 859167 332787 064740 904978 136733 226490 860366 333769 606763 487481 132448 411218 460864 283767 575079 238080 > 4²⁰⁷ [i]