MinT - Best Known (206−48, 206, s)-Nets in Base 4

Best Known (206−48, 206, s)-Nets in Base 4

(206−48, 206, 1040)-Net over F₄ — Constructive and digital

Digital (158, 206, 1040)-net over F₄, using

4² times duplication [i] based on digital (156, 204, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(206−48, 206, 2689)-Net over F₄ — Digital

Digital (158, 206, 2689)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−48, 206, 480734)-Net in Base 4 — Upper bound on s

There is no (158, 206, 480735)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10577 061503 770713 842539 199651 236994 200090 152799 335752 851585 820580 536581 499821 768281 988502 246551 892000 809522 702784 787093 141379 > 4²⁰⁶ [i]