MinT - Best Known (115, 115+35, s)-Nets in Base 4

Best Known (115, 115+35, s)-Nets in Base 4

(115, 115+35, 1036)-Net over F₄ — Constructive and digital

Digital (115, 150, 1036)-net over F₄, using

4² times duplication [i] based on digital (113, 148, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 37, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(115, 115+35, 2061)-Net over F₄ — Digital

Digital (115, 150, 2061)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+35, 452573)-Net in Base 4 — Upper bound on s

There is no (115, 150, 452574)-net in base 4, because

1 times m-reduction [i] would yield (115, 149, 452574)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509259 297472 643620 501762 813413 174468 405020 516808 680897 434426 800958 670813 823233 644726 648525 > 4¹⁴⁹ [i]