MinT - Best Known (111, 111+91, s)-Nets in Base 4

Best Known (111, 111+91, s)-Nets in Base 4

(111, 111+91, 130)-Net over F₄ — Constructive and digital

Digital (111, 202, 130)-net over F₄, using

t-expansion [i] based on digital (105, 202, 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]

(111, 111+91, 201)-Net over F₄ — Digital

Digital (111, 202, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+91, 2835)-Net in Base 4 — Upper bound on s

There is no (111, 202, 2836)-net in base 4, because

1 times m-reduction [i] would yield (111, 201, 2836)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 387588 835382 265441 310875 161969 766572 585306 528665 515646 837568 644343 047542 743784 258921 458471 598499 939317 275740 063533 895968 > 4²⁰¹ [i]