MinT - Best Known (107, 200, s)-Nets in Base 4

Best Known (107, 200, s)-Nets in Base 4

(107, 200, 130)-Net over F₄ — Constructive and digital

Digital (107, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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]

(107, 200, 181)-Net over F₄ — Digital

Digital (107, 200, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 200, 2376)-Net in Base 4 — Upper bound on s

There is no (107, 200, 2377)-net in base 4, because

1 times m-reduction [i] would yield (107, 199, 2377)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 657589 914929 998777 151475 546203 021757 246198 912628 249013 711317 467880 167678 933875 703593 719124 460639 899147 659132 023717 063328 > 4¹⁹⁹ [i]