MinT - Best Known (200−89, 200, s)-Nets in Base 4

Best Known (200−89, 200, s)-Nets in Base 4

(200−89, 200, 130)-Net over F₄ — Constructive and digital

Digital (111, 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]

(200−89, 200, 207)-Net over F₄ — Digital

Digital (111, 200, 207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−89, 200, 3003)-Net in Base 4 — Upper bound on s

There is no (111, 200, 3004)-net in base 4, because

1 times m-reduction [i] would yield (111, 199, 3004)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 653418 928634 321556 809643 200903 992729 890313 002614 043508 899670 262247 530918 076724 875259 146937 799483 106041 964949 050065 927884 > 4¹⁹⁹ [i]