MinT - Best Known (113, 113+71, s)-Nets in Base 4

Best Known (113, 113+71, s)-Nets in Base 4

(113, 113+71, 130)-Net over F₄ — Constructive and digital

Digital (113, 184, 130)-net over F₄, using

t-expansion [i] based on digital (105, 184, 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]

(113, 113+71, 307)-Net over F₄ — Digital

Digital (113, 184, 307)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+71, 6488)-Net in Base 4 — Upper bound on s

There is no (113, 184, 6489)-net in base 4, because

1 times m-reduction [i] would yield (113, 183, 6489)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 703643 364193 192787 925973 622390 509422 975373 068195 901042 964704 389137 627033 480737 820679 970209 449764 572965 202448 > 4¹⁸³ [i]