MinT - Best Known (137, 137+123, s)-Nets in Base 4

Best Known (137, 137+123, s)-Nets in Base 4

(137, 137+123, 130)-Net over F₄ — Constructive and digital

Digital (137, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(137, 137+123, 216)-Net over F₄ — Digital

Digital (137, 260, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+123, 2777)-Net in Base 4 — Upper bound on s

There is no (137, 260, 2778)-net in base 4, because

1 times m-reduction [i] would yield (137, 259, 2778)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 869122 990613 405886 315147 393708 983090 791849 069375 419756 104354 972943 975746 668057 447537 567926 255310 924260 973310 817024 380698 647535 536058 517749 304462 043318 331600 > 4²⁵⁹ [i]