MinT - Best Known (199−79, 199, s)-Nets in Base 4

Best Known (199−79, 199, s)-Nets in Base 4

(199−79, 199, 130)-Net over F₄ — Constructive and digital

Digital (120, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 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]

(199−79, 199, 298)-Net over F₄ — Digital

Digital (120, 199, 298)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−79, 199, 5814)-Net in Base 4 — Upper bound on s

There is no (120, 199, 5815)-net in base 4, because

1 times m-reduction [i] would yield (120, 198, 5815)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161562 492704 658441 249702 167500 470561 821173 705617 489154 773532 239968 174265 109329 243251 715470 875148 110658 218046 866170 719380 > 4¹⁹⁸ [i]