MinT - Best Known (108, 108+33, s)-Nets in Base 4

Best Known (108, 108+33, s)-Nets in Base 4

(108, 108+33, 1036)-Net over F₄ — Constructive and digital

Digital (108, 141, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (107, 140, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 35, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(108, 108+33, 1933)-Net over F₄ — Digital

Digital (108, 141, 1933)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+33, 420173)-Net in Base 4 — Upper bound on s

There is no (108, 141, 420174)-net in base 4, because

1 times m-reduction [i] would yield (108, 140, 420174)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 942672 140172 655815 828262 340116 644695 049081 249930 104386 515177 186123 934025 688602 067348 > 4¹⁴⁰ [i]