MinT - Best Known (106, 106+65, s)-Nets in Base 4

Best Known (106, 106+65, s)-Nets in Base 4

(106, 106+65, 130)-Net over F₄ — Constructive and digital

Digital (106, 171, 130)-net over F₄, using

t-expansion [i] based on digital (105, 171, 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]

(106, 106+65, 303)-Net over F₄ — Digital

Digital (106, 171, 303)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+65, 6706)-Net in Base 4 — Upper bound on s

There is no (106, 171, 6707)-net in base 4, because

1 times m-reduction [i] would yield (106, 170, 6707)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 242061 898814 977978 893389 991066 786461 379015 595978 327740 926846 515770 294742 619173 775326 906863 684050 136335 > 4¹⁷⁰ [i]