MinT - Best Known (201−49, 201, s)-Nets in Base 4

Best Known (201−49, 201, s)-Nets in Base 4

(201−49, 201, 1032)-Net over F₄ — Constructive and digital

Digital (152, 201, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (151, 200, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 50, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(201−49, 201, 2098)-Net over F₄ — Digital

Digital (152, 201, 2098)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−49, 201, 339925)-Net in Base 4 — Upper bound on s

There is no (152, 201, 339926)-net in base 4, because

1 times m-reduction [i] would yield (152, 200, 339926)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 582423 996089 001469 973724 045464 281546 868561 120164 565758 400544 508588 537659 166798 366256 694858 071338 577781 835283 687645 066216 > 4²⁰⁰ [i]