MinT - Best Known (116, 116+85, s)-Nets in Base 4

Best Known (116, 116+85, s)-Nets in Base 4

(116, 116+85, 130)-Net over F₄ — Constructive and digital

Digital (116, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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]

(116, 116+85, 246)-Net over F₄ — Digital

Digital (116, 201, 246)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+85, 4017)-Net in Base 4 — Upper bound on s

There is no (116, 201, 4018)-net in base 4, because

1 times m-reduction [i] would yield (116, 200, 4018)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 601819 441469 247645 056317 162690 262232 494026 634989 568360 255486 873348 528670 825789 304626 268415 123738 545686 887740 116171 626264 > 4²⁰⁰ [i]